Chapter 9, Problem 12RE

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# In Problems 7-20, find each limit, if it exists. 12.   lim x → − 1 2 x 2 − 1 4 6 x 2 + x − 1

To determine

To calculate: The value of the limit limx12x2146x2+x1.

Explanation

Given Information:

The provided limit is limxâ†’âˆ’12x2âˆ’146x2+xâˆ’1.

Formula used:

A limit limxâ†’cx can be simplified as,

limxâ†’cx=c

According to the property of difference of squares,

a2âˆ’b2=(a+b)(aâˆ’b)

Calculation:

Consider the provided limit,

limxâ†’âˆ’12x2âˆ’146x2+xâˆ’1

Simplify the limit by substituting âˆ’12 for x,

limxâ†’âˆ’12x2âˆ’146x2+xâˆ’1=(âˆ’12)2âˆ’146(âˆ’12)2+(âˆ’12)âˆ’1=14âˆ’146â‹…(14)+âˆ’1âˆ’22=032âˆ’32=00

Since, the limit has 00 indeterminate form at x=âˆ’12.

Thus, reduce the fraction, by factorizing the denominator and apply the property of difference of squares in numerator,

limxâ†’âˆ’12x2âˆ’(12)26x2+xâˆ’1=limxâ†’âˆ’12(xâˆ’12)(x+12)6x2+3xâˆ’2xâˆ’1=limxâ†’âˆ’12

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